MatSc503 Kinetics of Materials Processes - Test 1 February 24, 1999 1. (35 points) The phase diagram of a binary system (components A and B) is shown in the figure below. An infinite couple is made with pure B on one side and a finely dispersed twophase a
Solution to Problem #7 of Sample Exam Questions 7. In CaF2 , the predominant ionic defects are the anti-Frenkel defects whose concentrations are controlled from the following defect reaction:
FF V F + Fi'
and the equilibrium constant is given by ' K1 = V
Solutions to Test 1 MatSc 503 - Kinetics of Materials Processes Test date: February 25, 2002
1. A 1-mm-thick sheet of steel at 750C is subjected to conditions that maintain the carbon content at zero on one surface and at 3 at% carbon on the other surface
Sample Exam Questions
1. A piece of Steidlium (St) with a dimension 10cm 10cm 1cm containing 1.0 at % Deikium (De) is put into an oven for removing De. The density of St is 5g/cm3. The surface concentration of De is maintained at 0 at%. The diffusion coef
Kinetics of Phase Transformations
(References: J. W. Christian, Theory of Transformations in Metals and Alloys; Porter and Easterling, Phase Transformations in Metals and Alloys)
Change of state, e.g. s l , l v, l s Phase Transformations Change of structu
Coupling of Other Processes with Diffusion
Review of irreversible thermodynamics Generalized linear theory for coupled kinetic processes Thermoelectric phenomena Thermomigration Electromigration Diffusion in multicomponent systems
Irreversible Thermodyna
Self-Diffusion Through Vacancy Mechanism
Self-diffusion: diffusion of atoms in a pure material (e.g., Al atoms in pure Al) or binary and multicomponent compounds in which the diffusion of different atoms is limited to their own sublattices (e.g. Mg and O
(e) Electrons, holes, and ionization states of defects The process of forming intrinsic electron-hole pairs is excitation across the bandgap
null e'+ h
Their concentrations can be approximated as
E n = p = N c N v exp g 2kT
Nc effective conduction band
Kirkendall Effect and Chemical Diffusion
Up to this point, we have considered self-diffusion, tracer atom diffusion, and diffusion of small interstitial atoms in a host lattice of larger atoms. We usually assumed that the diffusion coefficient is a consta
Since the activation for diffusion along extended defects is smaller than that in the bulk, the diffusion along extended defects become increasingly important as temperature decreases Example lnD
Polycrystalline Ag Single crystal Ag 1/T
The ratio of the n
Diffusion in Homogeneous Concentrated Alloys
In a homogeneous concentrated alloy, two tracer diffusion coefficients can be defined, one for each species:
AB DA*
and
AB DB*
They can be measured through a thin-film experiments using tracer atoms. By varying
Thermodynamic Properties of Point Defects
(a) Single vacancy in elementary crystals The enthalpy (energy for constant volume) change by removing an atom inside a crystal and placing it on the surface is called the formation enthalpy (energy) of a vacancy,
Atomic Theory of Diffusion
(See Chapter 2 in Philibert)
The purpose: to relate the phenomenological diffusion coefficient to microscopic parameters such as jump distance and jump frequency Consider a simple problem of diffusion along [001] direction of a
At short times, many terms are required for obtaining the accurate concentration profile. However, at long times, a single term is sufficient as each successive term is smaller than the preceding one. Consider the ratio of the maximum values of the first
Square Root Relationship
For infinite or semi-infinite systems with constant surface concentration, the solution involves only the single dimensionless parameter
x 2 Dt
1. 2. 3. The distance of penetration of any given concentration is proportional to the
(2) Extended initial distributions, e.g., for the initial condition, c
c for x < 0 c( x,0 ) = o 0 for x > 0
co
d
x=0 x
Consider a line source of strength, co d
2 co d 1 2 exp 2(Dt ) 4 Dt
Superposition of the profiles from all elements,
c ( x, t ) =
2 co
Types of Solutions to Ficks Second Law
Error function solutions short-time or infinite systems
l (system size ) > Dt
Trigonometric function solutions long-time or finite systems
l (system size ) ~ Dt
Methods of solution: (1) Fourier transforms; (2) separa
Numerical Example Quasi-steady State
A cubic steel tank of volume 1 liter and wall thickness 0.1 cm is used to store hydrogen with an initial pressure of 8.7 atm. The tank is placed in outer space at 673 K. The hydrogen concentration on the steel surface
Ficks First Law
J = D c x
J flux of diffusing particles (molecules, atoms, ions, point defects, free electrons, electron holes, etc.). Flux has a direction. c x concentration gradient. D diffusion coefficient or diffusivity.
L2 c mole/L3 mole J 2 = D Un
Simultaneous Ordering and Phase Separation
'
+'
Ni
Al
Atomic structure
microstructure
Turbine Blade
Nucleation and Growth
G
Continuous transformations
Gn
Gg
Go
G p
A
BA
Microscopic diffusion equation simulation of phase separation
B
1
Nucleation and Gro
MatSc 503 Kinetics of Materials Processes Spring 2000 Problem Set #6, Due April 19 1. A given phase transformation, to , occurs by nucleating cuboidal precipitates of from the matrix at 700 K. If the lattices across the / interfaces are continuous, we cal
MatSc503 Kinetics of Materials Processes Problem Set #5 Due April 5 1. Two similar carbon-saturated molten pig irons, one containing 0.8% S and the other 0.8% S and 0.46% Si, are in separate experiments put in contact with the same sulfur-free slag at 150
MatSc503 Kinetics of Materials Processes HW 2
Due February 2, 2000
1. 1-7 in Shewmon: It is suggested that the change in hydrogen potential of an aqueous solution could be measured by the change in electrical resistance of an inert metal foil immersed in
MatSc503 Kinetics of Materials Processes
Due January 26, 2000
1. 1-2 in Shewmon 2. Part b of 1-4 in Shewmon 3. On silicon uniformly doped with 1015cm,3 atoms of arsenic, a very thin layer strongly doped with boron is deposited and capped by silicon nitrid
Solution to Problem Set #9 Problem 1. (a) Metal, M, undergoes an allotropic phase transformation between and at 1100 K. The low temperature phase is . A sample of M containing 108 cm-3 small oxide inclusions which act as effective nucleation sites even fo
Matsc 503 Kinetics of Materials Processes Spring 2002 Problem Set #9 Due: optional 1. (a) Metal, M, undergoes an allotropic phase transformation between and at 1100 K. The low temperature phase is . A sample of M containing 108 cm-3 small oxide inclusions
Solution to Problem Set #8 Problem A binary system A-B exhibits the regular solution behavior in the solid state. Answer parts (a) through (e), each when, o=(1/a)(da/dXA), the linear strain per unit composition difference, is equal to (i) 0 and (ii) 0.06.
Matsc 503 Kinetics of Materials Processes Spring 2002 Problem Set #8 Due April 17 A binary system A-B exhibits the regular solution behavior in the solid state. Answer parts (a) through (e), each when, o=(1/a)(da/dXA), the linear strain per unit compositi